A067018 Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (nim-sum a(i)+a(n-i)), where mex means smallest nonnegative missing number.

1, 4, 3, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0

Offset

0,2

Comments

Nim-sum is addition in base 2 without carry (XOR the binary expansions).

References

R. K. Guy, Unsolved Problems in Number Theory, E27.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Example

a(5) = mex{1 xor 0, 4 xor 2, 3 xor 3, etc. (duplicates)} = mex{1 xor 0, 100 xor 10, 11 xor 11} (in base 2) = mex{1, 6, 0} = 2

Prog

(Haskell)
import Data.Bits (xor)
import Data.List ((\\))
a067018 n = a067018_list !! n
a067018_list =  [1, 4, 3, 2] ++ f [2, 3, 4, 1] where
  f xs = mexi : f (mexi : xs) where
    mexi = head $ [0..] \\ zipWith xor xs (reverse xs) :: Integer
-- Reinhard Zumkeller, May 05 2012

Crossrefs

Cf. A067016, A067017.

Sequence in context: A349989 A067017 A258692 * A200233 A350493 A327351

Adjacent sequences: A067015 A067016 A067017 * A067019 A067020 A067021

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 17 2002

Extensions

More terms from John W. Layman, Feb 20 2002

Status

approved